Coordination number: Counting functions

Coordination number: Counting functions#

This module contains all the counting functions used throughout the projects of the Grimme group. This includes the following counting functions: - exponential (DFT-D3, EEQ) - error function (DFT-D4) - double exponential (GFN2-xTB)

Additionally, the analytical derivatives for the counting functions are also provided and can be used for checking the autograd results.

tad_mctc.ncoord.count.derf_count(r, r0, kcn=7.5)[source]#

Derivative of error function counting function w.r.t. the distance.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B).

  • kcn (Tensor | float | int, optional) – Steepness of the counting function. Defaults to tad_mctc.ncoord.defaults.KCN_D3.

Returns:

Derivative of count of coordination number contribution.

Return type:

Tensor

tad_mctc.ncoord.count.dexp_count(r, r0, kcn=16.0)[source]#

Derivative of the exponential counting function w.r.t. the distance.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B).

  • kcn (Tensor | float | int, optional) – Steepness of the counting function. Defaults to tad_mctc.ncoord.defaults.KCN_D3.

Returns:

Derivative of count of coordination number contribution.

Return type:

Tensor

tad_mctc.ncoord.count.dgfn2_count(r, r0, ka=10.0, kb=20.0, r_shift=2.0)[source]#

Exponential counting function for coordination number contributions as used in GFN2-xTB.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B) or cutoff radius.

  • ka (Tensor | float | int, optional) – Steepness of the first counting function. Defaults to tad_mctc.ncoord.defaults.KA.

  • kb (Tensor | float | int, optional) – Steepness of the second counting function. Defaults to tad_mctc.ncoord.defaults.KB.

  • r_shift (Tensor | float | int, optional) – Offset of the second counting function. Defaults to tad_mctc.ncoord.defaults.R_SHIFT.

Returns:

Count of coordination number contribution.

Return type:

Tensor

tad_mctc.ncoord.count.erf_count(r, r0, kcn=7.5)[source]#

Error function counting function for coordination number contributions.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B).

  • kcn (Tensor | float | int, optional) – Steepness of the counting function. Defaults to tad_mctc.ncoord.defaults.KCN_D3.

Returns:

Count of coordination number contribution.

Return type:

Tensor

tad_mctc.ncoord.count.exp_count(r, r0, kcn=16.0)[source]#

Exponential counting function for coordination number contributions.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B).

  • kcn (Tensor | float | int, optional) – Steepness of the counting function. Defaults to tad_mctc.ncoord.defaults.KCN_D3.

Returns:

Count of coordination number contribution.

Return type:

Tensor

tad_mctc.ncoord.count.gfn2_count(r, r0, ka=10.0, kb=20.0, r_shift=2.0)[source]#

Exponential counting function for coordination number contributions as used in GFN2-xTB.

Parameters:

  • r (Tensor) – Internuclear distances.

  • r0 (Tensor) – Covalent atomic radii (R_AB = R_A + R_B) or cutoff radius.

  • ka (Tensor | float | int, optional) – Steepness of the first counting function. Defaults to tad_mctc.ncoord.defaults.KA.

  • kb (Tensor | float | int, optional) – Steepness of the second counting function. Defaults to tad_mctc.ncoord.defaults.KB.

  • r_shift (Tensor | float | int, optional) – Offset of the second counting function. Defaults to tad_mctc.ncoord.defaults.R_SHIFT.

Returns:

Count of coordination number contribution.

Return type:

Tensor

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